Partial regularity for mass-minimizing currents in Hilbert spaces

publishedyear: 2015 journal: J. Reine Angew. Math. abstract: Recently, the theory of currents and the existence theory for Plateau's problem have been extended to the case of finite-dimensional currents in infinite-dimensional manifolds or even metric spaces; see [[[5|http://cvgmt.sns.it/paper/1519/]]] (and also [[[7|http://cvgmt.sns.it/paper/1762/],[37|http://arxiv.org/abs/1203.5330/]]] for the most recent developments). In this paper, in the case when the ambient space is Hilbert, we provide the first partial regularity result, in a dense open set of the support, for $n$-dimensional integral currents which locally minimize the mass. Our proof follows with minor variants [[[32|http://www.iumj.indiana.edu/IUMJ/FULLTEXT/1982/31/31035]]], implementing Lipschitz approximation and harmonic approximation without indirect arguments and with estimates which depend only on the dimension $n$ and not on codimension or dimension of the target space.